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The action functional for a family of diffusion fields in the plane

Authors:	V N Klepikov

Abstract:	For a random fieldx _st defeined by $x_{st}^\varepsilon = x + \smallint _0^s \smallint _0^t a(u,\upsilon ,\varepsilon ,x_{u\upsilon }^\varepsilon ) du d\upsilon + \varepsilon \smallint _0^s \smallint _0^t b(u,\upsilon ,x_{u\upsilon }^\varepsilon ) dw_{u\upsilon }$ , we find an explicit form for the action functional in the sense of Venttsel'-Freidlin.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 40–47, 1987.

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