mBm-Biblio-Mathematics

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How big are the increments of a multifractional brownian motion?.

L. Zhengyan
Science in China series A: Mathematics, No 10, vol. 45, pp 1291-1300, 2002

Some properties of a multifractional brownian motion.
Z. Lin, J. Zheng
Statistics & Probability letters, No 7, vol. 77, pp 687-692, 2007

A weak limit theorem for generalized multifractional brownian motion. 
H. Dai, Y. Li 
Statistics and Probability Letters, vol. 80, pp 348-356, 2010

A general framework for waves in random media with long-range correlations
Renaud Marty and Knut Sølna
Ann. Appl. Probab. Volume 21, Number 1 (2011), 115-139
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoap/1292598029

Approximation of multifractional Brownian motion by absolutely continuous processes
K. V. Ral’chenko
Teoriya Imovirnostei ta Matematichna Statistika, vipusk 82 (2010)
Theor. Probability and Math. Statist. No. 82 (2011), 115-127.
http://www.ams.org/journals/tpms/2011-82-00/S0094-9000-2011-00831-9/home.html

Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times
Antoine Ayache, Narn-Rueih Shieh, and Yimin Xiao
Ann. Inst. H. Poincare Probab. Statist Volume 47, Number 4 (2011), 1029-1054.
http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.aihp/1317906500&page=record

The covariance structure of multifractional Brownian motion, with application to long range dependence
A. Ayache, S. Cohen, J. Levy Vehel
2000 IEEE International Conference on Acoustics, Speech, and Signal Processing - ICASSP 2000 (2000)
http://hal.inria.fr/inria-00581032_v1/

Lacunary Fractional Brownian Motion
M Clausel
ESAIM P&S (2011) 10.1051/ps/2010014
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8034302

Approximation of the solution of stochastic differential equations driven
by multifractional Brownian motion
Anna So´os
Stud. Univ. Babe¸-Bolyai Math. 56(2011), No. 2, 587–598
www.cs.ubbcluj.ro/~studia-m/2011-2/soos-final.pdf

Weyl and Riemann–Liouville multifractional Ornstein–Uhlenbeck processes
S C Lim and L P

Teo 2007 J. Phys. A: Math. Theor. 40 6035
http://iopscience.iop.org/1751-8121/40/23/003;jsessionid=55C2BDD0D465935C8C53F3372BFEF008.c1

Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces
Hongshuai Dai
Journal of Applied Mathematics and Computing
http://www.springerlink.com/content/7p0238j7ut1902nt/

Real harmonizable multifractional Lévy motions
Céline Lacaux
Probability and Statistics, Volume 40, Issue 3, May-June 2004, Pages 259-277
http://www.sciencedirect.com/science/article/pii/S0246020303000645

Local time and Tanaka formula for a Volterra-type multifractional Gaussian process
Brahim Boufoussi, Marco Dozzi, and Renaud Marty
Bernoulli Volume 16, Number 4 (2010), 1294-1311
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bj/1290092907

Sample path properties of the local time of multifractional Brownian motion
Brahim Boufoussi, Marco Dozzi, and Raby Guerbaz
Bernoulli,Volume 13, Number 3 (2007), 849-867
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bj/1186503490

Integrated fractional white noise as an alternative to multifractional Brownian motion
Allan Sly
J. Appl, Prob, Volume 44, Number 2 (2007), 393-408
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jap/1183667409

Fractional Brownian motion and multifractional Brownian motion of Riemann-Liouville type
S C Lim
Journal of Physics A: Mathematical and General, 34 (7), p.1301-1310, Feb 2001
http://iopscience.iop.org/0305-4470/34/7/306/

Modeling of locally self-similar processes using multifractional Brownian motion of Riemann-Liouville type
Muniandy, S V, Lim, S C,
Physical review. E, Statistical, nonlinear, and soft matter physics, 63 (4 Pt 2), p.046104, Apr 2001
http://www.ncbi.nlm.nih.gov/pubmed/11308909?dopt=Abstract

Stochastic 2-microlocal analysis
Herbin, Erick, Lévy-Véhel, Jacques,
Stochastic Processes and their Applications, 119 (7), p.2277-2311, Jul 2009
http://www.sciencedirect.com/science/article/pii/S0304414908001725

Asymptotics of supremum distribution of α(t)-locally stationary Gaussian processes
Dȩbicki, Krzysztof, Kisowski, Paweł,
Stochastic Processes and their Applications, 118 (11), p.2022-2037, Nov 2008
http://www.sciencedirect.com/science/article/pii/S0304414907002153

Nonhomogeneous fractional integration and multifractional processes
Surgailis, Donatas,
Stochastic Processes and their Applications, 118 (2), p.171-198, Feb 2008
http://www.sciencedirect.com/science/article/pii/S0304414907000567

Functional limit theorems for generalized quadratic variations of Gaussian processes
Bégyn, Arnaud,
Stochastic Processes and their Applications, 117 (12), p.1848-1869, Dec 2007
http://www.sciencedirect.com/science/article/pii/S030441490700035X

Wavelet construction of Generalized Multifractional processes
Ayache, Antoine / Jaffard, Stéphane / Taqqu, Murad S. ,
Revista Matemática Iberoamericana, 23 (1), p.327-370, Apr 2007
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rmi/1180728896

Stochastic properties of the linear multifractional stable motion
Stoev, Stilian / Taqqu, Murad S. ,
Advances in Applied Probability, 36 (4), p.1085-1115, Dec 2004
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aap/1103662959

Multi-operator scaling random fields
Biermé, Hermine, Lacaux, Céline, Scheffler, Hans-Peter,
Stochastic Processes and their Applications, 121 (11), p.2642-2677, Nov 2011
http://www.sciencedirect.com/science/article/pii/S030441491100161X

Smoothness of Gaussian local times beyond the local nondeterminism
Boufoussi, Brahim / Guerbaz, Raby,
Stochastic Processes and their Applications, 119 (3), p.1001-1014, Mar 2009
http://www.sciencedirect.com/science/article/pii/S0304414908000756

Dimension results of multifractional Brownian sheets
Dongsheng Wu
J. Math. Phys. 48, 073511 (2007)
http://jmp.aip.org/resource/1/jmapaq/v48/i7/p073511_s1?isAuthorized=no

The fractional oscillator process with two indices
S C Lim, L P Teo ,
Journal of Physics A: Mathematical and Theoretical, 42 (6), p.065208, Feb 2009
http://iopscience.iop.org/1751-8121/42/6/065208/

Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation
S C Lim, L P Teo
J. Stat. Mech. (2009)
http://iopscience.iop.org/1742-5468/2009/08/P08015

Path properties of multifractal Brownian motion
K. V. Ral’chenko; G. M. Shevchenko
Theor. Probability and Math. Statist. No. 80 (2010), 119-130.
http://www.ams.org/journals/tpms/2010-80-00/S0094-9000-2010-00799-X/home.html

Real harmonizable multifractional stable process and its local properties
Marco Dozzi, Georgiy Shevchenko
Stochastic processes and their applications, 121(7), July 2011, p1509-1523
http://www.sciencedirect.com/science/article/pii/S0304414911000718

Invariance principle, multifractional Gaussian processes and long-range dependence
Serge Cohen and Renaud Marty
Ann. Inst. H. Poincaré Probab. Statist. Volume 44, Number 3 (2008), 475-489
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aihp/1211819421

The Generalized Multifractional Field: A Nice Tool for the Study of the Generalized Multifractional Brownian Motion
Antoine Ayache
Journal of Fourier Analysis and Applications, Volume 8, Number 6, 581-602
http://www.springerlink.com/content/7n42u2y0fp36hmat/

A generalized Cauchy process and its application to relaxation phenomena
S C Lim, Ming Li
2006 J. Phys. A: Math. Gen. 39
http://iopscience.iop.org/0305-4470/39/12/005

Multifractional processes with random exponent
Antoine Ayache, Murad S. Taqqu
Publ. Mat. 49 (2005), 459–486
http://ddd.uab.cat/pub/pubmat/02141493v49n2p459.pdf

Series representation and simulation of multifractional Lévy motions
Céline Lacaux
Adv. in Appl. Probab. Volume 36, Number 1 (2004), 171-197
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aap/1077134469

Inference on Fractal Processes Using Multiresolution Approximation
Kenneth Falconer , Carmen Fernández
Biometrika (2007) 94 (2): 313-334
http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.1250

A process very similar to multifractional Brownian motion
Antoine Ayache, Pierre R. Bertrand
Recent Developments in Fractals and Related Fields (2010) 311--326
http://arxiv.org/abs/0901.2808

Local times of multifractional Brownian sheets
Mark Meerschaert, Dongsheng Wu, Yimin Xiao
Bernoulli 2008, Vol. 14, No. 3, 865-898
http://arxiv.org/abs/0810.4438

Multifractional, multistable, and other processes with prescribed local form
K.J. Falconer, J. Levy Vehel
Journal of Theoretical Probability
http://arxiv.org/abs/0802.0645

From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions
E Herbin
Rocky Mountain J. Math. Volume 36, Number 4 (2006), 1249-1284
http://arxiv.org/abs/math/0503182

How rich is the class of multifractional brownian motions ?
Stilian A. Stoev, Murad S. Taqqu

 P. Zhuang, F. Liu, V. Anh, I. W. Turner

 http://eprints.qut.edu.au/29755/

Boufoussi, B., Lakhel, E., Dozzi, M.

Stochastic Analysis and Applications, 23(4), 665-685, 2005

Hu Sheng, YangQuan Chen, TianShuang Qiu

Dai Hongshuai, Li Yuqiang

 http://spie.org/x648.html?product_id=217584

From Constructive Field Theory to Fractional Stochastic Calculus. (I) An introduction: Rough Path Theory and Perturbative Heuristics

Jacques Magnen and Jérémie Unterberger

Annales Heri Poincare, 12(6), 1199-1226, 2011

http://www.springerlink.com/content/p34r03l6457384kn/

Random Fields Arising in Chaotic Systems: Burgers Equation and Fractal Pseudodifferential Systems

Nikolai N. Leonenko and M. Dolores Ruiz-Medina

Advances and Challenges in Space-time Modelling of Natural Events. Lecture Notes in Statistics, Vol. 207, pp.165-219, 2012

http://www.springerlink.com/content/t456266vg6046807/

2-microlocal analysis of martingales and stochastic integrals

Paul Balança and Erick Herbin

Stochastic Processes and their Applications, Vol. 122(6), pp. 2346-2382, 2012

http://www.sciencedirect.com/science/article/pii/S0304414912000440

Mixed stochastic differential equations with long-range dependence: Existence, uniqueness and convergence of solutions

Yuliya Mishura and Georgiy Shevchenko

Computers and mathematics with applications, ELSEVIER (In press)

http://www.sciencedirect.com/science/article/pii/S0898122112002660

Accelerating and retarding anomalous diffusion

Chai Hok Eab and S C Lim

Journal of Physics A: Mathematical and Theoretical, Vol. 45(14), 2012

http://iopscience.iop.org/1751-8121/45/14/145001/

Random Fields with Multifractional Regularity Order on Heterogenous Fractal Domains

M. D. Ruiz-Medina, V. V. Anh,  J. M. Angulo

Stochastic Analysis and Applications, Vol. 30 (5), 2012

http://www.tandfonline.com/doi/abs/10.1080/07362994.2012.704851

The two-parameter Volterra multifractional process

Ibrahima Mendy

Statistics & Probability Letters, Vol. 82 (12), pp.2115-2124, 2012 http://www.sciencedirect.com/science/article/pii/S0167715212002933

Continuous Gaussian Multifractional Processes with Random Pointwise Hölder Regularity

Antoine Ayache

Journal of Theoretical Probability, 2012

http://www.springerlink.com/content/m3378076n85042m2/

Linear Multifractional Stochastic Volterra Integro-Differential Equations

N. Tien Dung

http://tjm.math.ntu.edu.tw/~journal/tjm/preview4/m016(2012-07-26)1728.pdf

Local time of a multifractional Gaussian process
A. Sghir
Communications on Stochastic Analysis 2013, Volume 7, No. 4 pp 523-533

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