基本介紹
- 中文名:平穩點過程
- 外文名:stationary point process
- 所屬學科:數學
- 所屬問題:隨機過程(隨機點過程與分支過程)
- 相關概念:隨機點過程
基本介紹,相關定理及證明,
基本介紹
應當指出,有些文獻把這一術語用於對任意有限多個區間,其增量有平穩聯合分布的點過程。即對任意整數
和實數
和
,增量
![](/img/9/240/1454c5a00a285b28ce59e1daf65c.jpg)
![](/img/9/348/47451eec9e8b28f51a566bc9e5c7.jpg)
![](/img/f/3cf/d6c5214b141106300f2153096812.jpg)
![](/img/4/825/1dc54d527e84cb98c03e393a1335.jpg)
相關定理及證明
定理1 除了對一切
有
的平凡情形以外,對任意平穩點過程有
![](/img/1/33d/44e4255387eb0d725cbcd881add1.jpg)
![](/img/7/ca8/dd8424700dc5c4ddb89f313943ca.jpg)
![](/img/1/415/2f7a48ec8f8e51df5291741930df.jpg)
![](/img/9/c0d/ae6293580fb6a22e9d3540b2761d.jpg)
證明: 令
且注意到
取非負值,且非減,又
![](/img/9/c2e/0d0348337acbb355bc0d6392ab80.jpg)
![](/img/1/a3d/3a49cdb8c8e6e8b76e2a0880296d.jpg)
![](/img/7/7c2/d9a626b6d0cce238f60ef5ca169d.jpg)
![](/img/d/d3e/924e4f78b6b6784a76ea129146b5.jpg)
![](/img/4/bf4/70fb7aedb13b2f23fb29b9738cc6.jpg)
![](/img/c/e4d/bdb0146734ce66d7339120ae35a8.jpg)
![](/img/9/f09/9c44bd236e94026965439a29c95c.jpg)
![](/img/4/bf4/70fb7aedb13b2f23fb29b9738cc6.jpg)
![](/img/2/dc6/d30fbe63c9f43ee3b8efe4f14819.jpg)
![](/img/4/6ec/3c92555b40c35e0abe249df3c311.jpg)
![](/img/6/87d/14514be657818d3c33f1b16040a4.jpg)
![](/img/9/97b/0a227f4ab44c1c217d5f3aa76541.jpg)
![](/img/9/732/03600a5bef9c2b709b6edb3f7d9a.jpg)
![](/img/0/16c/71b179a2474ba00ee8bee71c4573.jpg)
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![](/img/9/a3f/a57f5483d04ff1c0f60bb6dc01e1.jpg)
![](/img/d/ffd/a2dd9b5e360b95ce08cc867724a5.jpg)
![](/img/3/559/bd8dba7d382577bf81068a7145bc.jpg)
![](/img/9/e9b/55b8ea8e6b0298cbc731ba808619.jpg)
![](/img/f/fa0/504d7e54d3d66b9a702e9db1925b.jpg)
![](/img/3/606/194d143408fdda8369919a9f911e.jpg)
![](/img/e/68f/543890b9eec6e48e7ad873cd3b96.jpg)
![](/img/6/6a2/39c99b07b5075bff591d086e8617.jpg)
![](/img/8/033/90e573e51d4d29b82996e6fc6e05.jpg)
現在假定
,此時,固定任意很大的A>0,取s使
,則由式(3)推出對一切
有
![](/img/1/446/16525c4cd54f0d493f8de4c82d60.jpg)
![](/img/9/2c2/8959db4c35982ca8387c20a80989.jpg)
![](/img/3/b6f/1dd4c6a135f907c41e5ee645d9a4.jpg)
![](/img/5/6a1/7b8c9125c91026fd46bf9f9f8daf.jpg)
![](/img/8/890/a6695763791f43693c996bf8adce.jpg)