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I'd like to solve a function [tex]W_{t}^{x}[/tex] from a recursive formula below.

[tex]W_{t}^{x}=P_{t}^{x}*W_{t+1}^{x+1}+(1 - P_{t}^{x})*W_{t+1}^{x}[/tex],

where [tex]P_{t}^{x} = \frac{E[\theta^{x+1}*(1 - \theta)^{t-x}]}{E[\theta^{x}*(1-\theta)^{t-x}]}[/tex], [tex]{\underset{t\to\infty, x\to 0}{lim}}W_{t}^{x} =0[/tex]. Here [tex]E[/tex] stands for expectation.

Any suggestions? Thanks.

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# Find a function from a Recursive Formula

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