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list1
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Joined: July 22nd, 2015, 2:12 pm

Re: help to prove a simple inequality

August 18th, 2016, 5:07 pm

What did I need is to take a difference between discrete time approximations of the first exit time in two different points t , x. I used approximation of the first exit time in the form. Then the difference will be reduced to the difference of two products of indicators. 

[$] \tau_{ t x } ( \lambda)  =   \sum_{k = 1}^{n} t_k \, I_{\bar{D}} \, ( \xi ( t_k ; t , x )) \prod_{j = 1}^{k - 1}  I_{D} \, ( \xi ( t_j ; t , x ))   [$] 
Here D is an open domain and t j are a fixed partition of the [ t , T ].
 
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Cuchulainn
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Re: help to prove a simple inequality

August 19th, 2016, 12:18 pm

What did I need is to take a difference between discrete time approximations of the first exit time in two different points t , x. I used approximation of the first exit time in the form. Then the difference will be reduced to the difference of two products of indicators. 

[$] \tau_{ t x } ( \lambda)  =   \sum_{k = 1}^{n} t_k \, I_{\bar{D}} \, ( \xi ( t_k ; t , x )) \prod_{j = 1}^{k - 1}  I_{D} \, ( \xi ( t_j ; t , x ))   [$] 
Here D is an open domain and t j are a fixed partition of the [ t , T ].
Undefined terms.

My idea would be to post the full proof of the theorem you want to prove, and go through it line-by-line.
 
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list1
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Joined: July 22nd, 2015, 2:12 pm

Re: help to prove a simple inequality

August 19th, 2016, 11:22 pm

What did I need is to take a difference between discrete time approximations of the first exit time in two different points t , x. I used approximation of the first exit time in the form. Then the difference will be reduced to the difference of two products of indicators. 

[$] \tau_{ t x } ( \lambda)  =   \sum_{k = 1}^{n} t_k \, I_{\bar{D}} \, ( \xi ( t_k ; t , x )) \prod_{j = 1}^{k - 1}  I_{D} \, ( \xi ( t_j ; t , x ))   [$] 
Here D is an open domain and t j are a fixed partition of the [ t , T ].
Undefined terms.

My idea would be to post the full proof of the theorem you want to prove, and go through it line-by-line.
Cuchullain, these days I am trying to refresh my math and look through last results before I began study derivatives. I had some plans but derivatives took my attention in full. Besides I have not had enough time for thinking about two different areas. Before an attempt to make new step I am reading results published in my book which should be the initial basis.