L-q (L-p)-theory of stochastic differential equations

Xia P, Xie L, Zhang X, Zhao G (2020)
STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130(8): 5188-5211.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Xia, Pengcheng; Xie, Longjie; Zhang, Xicheng; Zhao, GuohuanUniBi
Abstract / Bemerkung
In this paper we show the weak differentiability of the unique strong solution with respect to the starting point x as well as Bismut-Elworthy-Li's derivative formula for the following stochastic differential equation in R-d : dX(t) = b(t, X-t)dt + sigma(t, X-t)dW(t), X-0 =x, where sigma is bounded, uniformly continuous and nondegenerate, b is an element of (L) over tilde (p1)(q1) and del sigma is an element of (L) over tilde (p2)(q2) for some Pi, qi is an element of [2, infinity) with d/pi + 2/qi < 1, i = 1, 2, where <(L)over tilde>(pi)(qi) (,) i = 1, 2 are some localized spaces of L-qi (R+; L-pi (R-d)). Moreover, in the endpoint case b is an element of (L) over tilde (d;uni)(infinity) subset of (L) over tilde (d)(infinity), we also show the weak well-posedness. (C) 2020 Elsevier B.V. All rights reserved.
Stichworte
Krylov's estimate; L-q(L-p)-estimates; Zvonkin's transformation; duality
Erscheinungsjahr
2020
Zeitschriftentitel
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Band
130
Ausgabe
8
Seite(n)
5188-5211
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2944504

Zitieren

Xia P, Xie L, Zhang X, Zhao G. L-q (L-p)-theory of stochastic differential equations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2020;130(8):5188-5211.
Xia, P., Xie, L., Zhang, X., & Zhao, G. (2020). L-q (L-p)-theory of stochastic differential equations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(8), 5188-5211. doi:10.1016/j.spa.2020.03.004
Xia, P., Xie, L., Zhang, X., and Zhao, G. (2020). L-q (L-p)-theory of stochastic differential equations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130, 5188-5211.
Xia, P., et al., 2020. L-q (L-p)-theory of stochastic differential equations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(8), p 5188-5211.
P. Xia, et al., “L-q (L-p)-theory of stochastic differential equations”, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 130, 2020, pp. 5188-5211.
Xia, P., Xie, L., Zhang, X., Zhao, G.: L-q (L-p)-theory of stochastic differential equations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 130, 5188-5211 (2020).
Xia, Pengcheng, Xie, Longjie, Zhang, Xicheng, and Zhao, Guohuan. “L-q (L-p)-theory of stochastic differential equations”. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130.8 (2020): 5188-5211.

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