1 |
T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, Occupation time limits of inhomogeneous Poisson systems of independent particles, Stochastic Process. Appl. 118 (2008), no. 1, 28-52. https://doi.org/10.1016/j.spa.2007.03.008
DOI
|
2 |
T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, Self-similar stable processes arising from high-density limits of occupation times of particle systems, Potential Anal. 28 (2008), no. 1, 71-103. https://doi.org/10.1007/s11118-007-9067-z
DOI
|
3 |
N. Chakravarti and K. L. Sebastian, Fractional Brownian motion model for polymers, Chem. Phys. Lett. 267 (1997), no. 1-2, 9-13.
DOI
|
4 |
J. Cherayil and P. Biswas, Path integral description of polymers using fractional Brownian walks, J. Chem. Phys. 99 (1993), no. 11, 9230-9236.
DOI
|
5 |
M. Cranston and Y. Le Jan, Self-attracting diffusions: two case studies, Math. Ann. 303 (1995), no. 1, 87-93. https://doi.org/10.1007/BF01460980
DOI
|
6 |
T. E. Duncan, Y. Hu, and B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion. I. Theory, SIAM J. Control Optim. 38 (2000), no. 2, 582-612. https://doi.org/10.1137/S036301299834171X
DOI
|
7 |
R. T. Durrett and L. C. G. Rogers, Asymptotic behavior of Brownian polymers, Probab. Theory Related Fields 92 (1992), no. 3, 337-349. https://doi.org/10.1007/BF01300560
DOI
|
8 |
J. Garzon, Convergence to weighted fractional Brownian sheets, Commun. Stoch. Anal. 3 (2009), no. 1, 1-14. https://doi.org/10.31390/cosa.3.1.01
|
9 |
J. Guo, Y. Hu, and Y. Xiao, Higher-order derivative of intersection local time for two independent fractional Brownian motions, J. Theoret. Probab. 32 (2019), no. 3, 1190-1201. https://doi.org/10.1007/s10959-017-0800-2
DOI
|
10 |
S. Herrmann and B. Roynette, Boundedness and convergence of some self-attracting diffusions, Math. Ann. 325 (2003), no. 1, 81-96. https://doi.org/10.1007/s00208-002-0370-0
DOI
|
11 |
T. Mountford and P. Tarres, An asymptotic result for Brownian polymers, Ann. Inst. Henri Poincare Probab. Stat. 44 (2008), no. 1, 29-46. https://doi.org/10.1214/07-AIHP113
DOI
|
12 |
Y. Hu and B. Oksendal, Chaos expansion of local time of fractional Brownian motions, Stochastic Anal. Appl. 20 (2002), no. 4, 815-837. https://doi.org/10.1081/SAP-120006109
DOI
|
13 |
A. Jaramillo and D. Nualart, Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion, Stochastic Process. Appl. 127 (2017), no. 2, 669-700. https://doi.org/10.1016/j.spa.2016.06.023
DOI
|
14 |
P. Jung and G. Markowsky, On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion, Stochastic Process. Appl. 124 (2014), no. 11, 3846-3868. https://doi.org/10.1016/j.spa.2014.07.001
DOI
|
15 |
P. Jung and G. Markowsky, Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative, J. Theoret. Probab. 28 (2015), no. 1, 299-312.
DOI
|
16 |
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, 113, Springer-Verlag, New York, 1988. https://doi.org/10.1007/978-1-4684-0302-2
|
17 |
L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Vol. 2, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1987.
|
18 |
G. Shen and Q. Chen, Derivative for the intersection local time of weighted fractional Brownian motion, Submitted.
|
19 |
S. Herrmann and M. Scheutzow, Rate of convergence of some self-attracting diffusions, Stochastic Process. Appl. 111 (2004), no. 1, 41-55. https://doi.org/10.1016/j.spa.2003.10.012
DOI
|
20 |
G. Shen, L. Yan, and J. Cui, Berry-Esseen bounds and almost sure CLT for quadratic variation of weighted fractional Brownian motion, J. Inequal. Appl. 2013 (2013), 275, 13 pp. https://doi.org/10.1186/1029-242X-2013-275
DOI
|
21 |
G. Shen, X. Yin, and L. Yan, Least squares estimation for Ornstein-Uhlenbeck processes driven by the weighted fractional Brownian motion, Acta Math. Sci. Ser. B (Engl. Ed.) 36 (2016), no. 2, 394-408. https://doi.org/10.1016/S0252-9602(16)30008-X
|
22 |
X. Sun and L. Yan, Central limit theorems and parameter estimation associated with a weighted-fractional Brownian motion, J. Statist. Plann. Inference 192 (2018), 45-64. https://doi.org/10.1016/j.jspi.2017.07.001
DOI
|
23 |
X. Sun, L. Yan, and Q. Zhang, The quadratic covariation for a weighted fractional Brownian motion, Stoch. Dyn. 17 (2017), no. 4, 1750029, 41 pp. https://doi.org/10.1142/S0219493717500290
DOI
|
24 |
L. Yan, Derivative for the intersection local time of fractional Brownian motions, Preprint, 2016.
|
25 |
L. Yan, Y. Sun, and Y. Lu, On the linear fractional self-attracting diffusion, J. Theoret. Probab. 21 (2008), no. 2, 502-516. https://doi.org/10.1007/s10959-007-0113-y
DOI
|
26 |
L. Yan, Z. Wang, and H. Jing, Some path properties of weighted-fractional Brownian motion, Stochastics 86 (2014), no. 5, 721-758. https://doi.org/10.1080/17442508.2013.878345
DOI
|
27 |
L. Yan and X. Yu, Derivative for self-intersection local time of multidimensional fractional Brownian motion, Stochastics 87 (2015), no. 6, 966-999. https://doi.org/10.1080/17442508.2015.1019883
DOI
|
28 |
T. Bojdecki, L. G. Gorostiza, and A. Talarczyk, Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems, Electron. Comm. Probab. 12 (2007), 161-172. https://doi.org/10.1214/ECP.v12-1272
DOI
|
29 |
E. Alos, O. Mazet, and D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2001), no. 2, 766-801. https://doi.org/10.1214/aop/1008956692
DOI
|
30 |
S. M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973/74), 69-94. https://doi.org/10.1512/iumj.1973.23.23006
DOI
|