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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 37, Issue 1, Pages 25 - 38 (February 2010)


EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NON-LIPSCHITZ ANTICIPATING VOLTERRA EQUATIONS

Xiangfeng Yin and Qingchoo Xiao

Received August 10, 2009

References:



[1] E. Alòs and D. Nualart, Anticipating stochastic Volterra equations, Stochastic Process. Appl. 72(1) (1997), 73-95.

[2] L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, 1972.

[3] D. Barbu and G. Bocşan, Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients, Czechoslovak Math. J. 52(1) (2002), 87-95.

[4] M. A. Berger and V. J. Mizel, An extension of the stochastic integral, Ann. Probab. 10(2) (1982), 435-450.

[5] T. Caraballo, Asymptotic exponential stability of stochastic partial differential equations with delay, Stochastics Stochastics Rep. 33(1-2) (1990), 27-47.

[6] M. Eddahbi and M. Erraoui, On quasi-linear parabolic SPDEs with non-Lipschitz coefficients, Random Oper. Stochastic Equations 6(2) (1998), 105-126.

[7] J. A. León and D. Nualart, Stochastic evolution equations with random generators, Ann. Probab. 26(1) (1998), 149-186.

[8] J. A. León and D. Nualart, Anticipating integral equations, Potential Anal. 13(3) (2000), 249-268.

[9] Yu. Mishura and G. Shevchenko, Approximate solutions to anticipative stochastic differential equations, Statist. Probab. Lett. 78(1) (2008), 60-66.

[10] D. Nualart, The Malliavin Calculus and Related Topics, 2nd ed., Springer, 2006.

[11] É. Pardoux and P. Protter, Stochastic Volterra equations with anticipating coefficients, Ann. Probab. 18(4) (1990), 1635-1655.

[12] H. Qiao and X. Zhang, Homeomorphism flows for non-Lipschitz stochastic differential equations with jumps, Stochastic Process. Appl. 118(12) (2008), 2254-2268.

[13] C. A. Tudor, Itô-Skorohod stochastic equations and applications to finance, J. Appl. Math. Stoch. Anal. 2004(4) (2004), 359-369.

Keywords and phrases: anticipating stochastic calculus, Skorohod integral, stochastic Volterra equations, non-Lipschitz.

 


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