scholarly journals Stochastic differential equations with Sobolev drifts and driven by $\alpha$-stable processes

2013 ◽  
Vol 49 (4) ◽  
pp. 1057-1079 ◽  
Author(s):  
Xicheng Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stable Processes ◽  
Alpha Stable Processes

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

scholarly journals Regularity of solutions to anisotropic nonlocal equations

2020 ◽  
Vol 296 (3-4) ◽  
pp. 1135-1155 ◽  
Author(s):  
Jamil Chaker
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Harmonic Functions ◽  
Regularity Of Solutions ◽  
Hölder Regularity ◽  
Stable Processes ◽  
Symmetric Stable Processes ◽  
One Dimensional ◽  
Nonlocal Equations ◽  
Bounded Harmonic Functions

Abstract We study harmonic functions associated to systems of stochastic differential equations of the form $$dX_t^i=A_{i1}(X_{t-})dZ_t^1+\cdots +A_{id}(X_{t-})dZ_t^d$$ d X t i = A i 1 ( X t - ) d Z t 1 + ⋯ + A id ( X t - ) d Z t d , $$i\in \{1,\dots ,d\}$$ i ∈ { 1 , ⋯ , d } , where $$Z_t^j$$ Z t j are independent one-dimensional symmetric stable processes of order $$\alpha _j\in (0,2)$$ α j ∈ ( 0 , 2 ) , $$j\in \{1,\dots ,d\}$$ j ∈ { 1 , ⋯ , d } . In this article we prove Hölder regularity of bounded harmonic functions with respect to solutions to such systems.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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